Necessary Conditions for Optimality in Problems with Nonstandard Cost Functionals
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Usual formulation of optimal control problems involves the minimization of a cost functional which is of the form of a definite integral. In this chapter we develop necessary conditions for an optimal control in the case of problems in which the cost functional is either a quotient or a product of definite integrals. We call such functionals nonstandard, and these naturally arise in Chapters 2,4, and 5 during the computation of the performance of a suboptimal H∞ controller. In Chapters 2,4, and 5 a criterion for the evaluation of the cost functional will be presented in the specialized case of linear systems and quadratic integrands. Preliminary results for problems having a fixed final time and free terminal state are in . Related results can also be found in [2,3]. In this monograph, we consider only fixed final time problems. Problems in which the final time is free are treated in . In Section 5, we discuss the relation of our results to those in [2,3].
KeywordsOptimal Control Problem Final Time Tangent Direction Dual Cone Finite Horizon
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